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The driving force behind convolutional networks - the most successful deeplearning architecture to date, is their expressive power. Despite its wideacceptance and vast empirical evidence, formal analyses supporting this beliefare scarce. The primary notions for formally reasoning about expressiveness areefficiency and inductive bias. Expressive efficiency refers to the ability of anetwork architecture to realize functions that require an alternativearchitecture to be much larger. Inductive bias refers to the prioritization ofsome functions over others given prior knowledge regarding a task at hand. Inthis paper we overview a series of works written by the authors, that throughan equivalence to hierarchical tensor decompositions, analyze the expressiveefficiency and inductive bias of various convolutional network architecturalfeatures (depth, width, strides and more). The results presented shed light onthe demonstrated effectiveness of convolutional networks, and in addition,provide new tools for network design.

Analysis and Design of Convolutional Networks via Hierarchical Tensor Decompositions